First, it is important to point out that folk legends about unicorns do not generally exist. The European peasantry simply did not believe in them and did not tell stories about encounters with them. They told stories about encountering fairies, mermaids (or seal people), and trolls, and they told about the distant past existence of creatures such as giants and dragons. But unicorns are virtually absent from material gathered from the folk.

The unicorn was an abstraction of the intelligentsia. While many fantastic creatures that appear in literature drew inspiration from the illiterate folk, a few like the unicorn were strictly literary (one often encounters exotic beasts in medieval bestiaries, but many of these were not popularly seen to exist).

Obviously reports of sightings of creatures in exotic settings that seemed like unicorns or the importation of a narwhal tusk could serve to confirm the existence of unicorns, but this would have been something entertained at court, not in the field. Consider this source for a general overview.

edit to correct typo.